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HISTORY OP PHYSICAL ASTRONOMY.
We owe to Eratosthenes , another of the astronomers who observed atAlexandria, the earliest determination of one of the most importantelements of astronomical science. This astronomer is said to have mea-sured the distance between the tropics, and to have found it to be equalto -iA parts of the circumference of the circle. This gives 23° 51' 19".5for the obliquity of the ecliptic—a result which exhibits a remarkable agree-ment with that assigned by the theory of gravitation, as the true value ofthe element, in the age of Eratosthenes .
It is manifest that neither the distances of the stars from the equator,nor the obliquity of the ecliptic, could have been determined even roughlywithout the use of instruments. The information which Ptolemy hassupplied upon this subject is exceedingly scanty. In treating of the ob-liquity of the ecliptic, he describes an instrument* for determining themeridional altitude of the sun. It was composed of two concentric circles,placed exactly in the plane of the meridian, one of which revolved withinthe other about their common centre. The inner circle carried two smallprisms attached to the opposite extremities of a diameter, and when thesun was on the meridian, it was turned round until the shadow of theupper prism fell exactly upon the lower one. An index, affixed to thelatter, then marked upon the graduated limb of the outer circle themeridional altitude of the sun *. It was, in all probability, by means ofan instrument of this construction that Eratosthenes determined thealtitude of the sun at each of the solstices, and hence deduced the distancebetween the tropics, the half of which distance gives the obliquity of theecliptic.
From the observed altitudes of the sun at the summer and winter solstices,it was easy to infer the position of the equator in the celestial sphere. Inorder to ascertain the passage of the sun through the equinox, a circular ringof metal was disposed in the plane of the equator, and the shadow of theupper half was watched until it fell upon the inner or concave surface ofthe lower half. As the shadow did not cover the entire breadth of thesurface on which it fell, it is manifest that the instant when the surface wasequally illuminated on each side of the shadow, indicated the presence ofthe sun in the plane of the equator. Ptolemy cites a passage from Hip-parchus , in which that astronomer refers to tw r o circles of this descriptionthat were used at Alexandria for observing the passage of the sun throughthe equinoxes. They were constructed of copper, and were placed in thesquare portico of the Museum j-.
Ptolemy has given no account of the instrument by means of whichthe earlier astronomers determined the distances of the stars fromthe equator. It in all probability resembled, in principle, the astrolabewhich Hipparchus employed at a subsequent period in observing the stars,only it was more simple in construction, since the use of it was confinedto one measurement relative to each star. In fact, if we suppose a circleto be placed in the plane of the equator, and another circle of equal mag-nitude to be movable around its poles, the distance of each star from theequator would be ascertained by turning the latter circle round until thestar appeared in its plane, and then noting the place of the star on itsdivided limb.
Whatever credit may be due to the earlier astronomers of the Ac-quainted with any method of reducing the motion of the sun to calculation until Hippar-chus undertook his researches on the subject.